Pakistan, set a modest 176-run target, were undone by a shambolic batting display as they lost their last seven wickets for just 41 runs after being on course for victory at 130-3 on Monday.
Left-arm spinner Ajaz Patel had a dream debut for New Zealand as he picked up 5-59 on a turning Sheikh Zayed Stadium pitch.
Arthur said Pakistan were hurting from the defeat.
"This is probably one of the worst defeats I have ever suffered in my career," Arthur, who also coached South Africa and Australia, told AFP.
"Everyone from myself as head coach to the players and the staff are hurting but we will use this defeat as a motivation to give ourself every opportunity to win the second game," vowed Arthur.
The victory gave New Zealand a 1-0 lead in the three-match series and was the fifth narrowest win by runs in Test cricket's history.
Arthur said his batsmen's shot selection was poor, having needed 139 on day four with all ten wickets intact.
New Zealand grabbed three quick wickets in the space of eight balls before Azhar Ali (65) and Asad Shafiq (45) added 82 runs for the fourth wicket.
Arthur refused to accept his batsmen were complacent.
"There was no complacency, I can certainly say," said Arthur, under whom Pakistan have now lost 13 of their 23 Tests, with nine wins and one draw.
"The guys tried unbelievably hard and everyone was disappointed from the decision of shot selection under pressure. We need to learn from this and move forward very, very quickly."
Arthur also bemoaned his side's continued failure to chase small targets, after also falling short in a chase of 136 against Sri Lanka last year at the same venue.
"The most disappointing thing was that it happened against Sri Lanka last year as well," he said.
"That's the thing the batting unit needs to get over and that we need to chase down targets in fourth innings," said Arthur, before pointing to Pakistan's failure to get a bigger first-innings lead than the 74 they managed after New Zealand's 153.
"We left ourselves too much to do in the fourth innings. We had that opportunity to nail this game off in the first innings but we let that go."
Arthur also defended batting coach Grant Flower, who has been in the role since 2014.
"Grant works incredibly hard with the batsmen and his level of commitment and the work and efforts he put in is second to none."